An object with a mass of $5 k g$ $5 kg$ is hanging from an axle with a radius of $12 c m$ $12 cm$ . If the wheel attached to the axle has a radius of $38 c m$ $38 cm$ , how much work would it take to turn the wheel a length equal to the circumference of the axle?

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An object with a mass of $5 k g$ $5 kg$ is hanging from an axle with a radius of $12 c m$ $12 cm$ . If the wheel attached to the axle has a radius of $38 c m$ $38 cm$ , how much work would it take to turn the wheel a length equal to the circumference of the axle?

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Answer 1 · 2016-04-23T10:17:55

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As shown in the figure
The radius of the Wheel $R = 38 c m$ $R=38cm$
The radius of the Axle $r = 12 c m$ $r=12cm$
The mass of the object $m = 5 k g$ $m=5kg$
The Weightof the object $W = m g = 5 \times 9.8 N$ $W=mg=5xx9.8N$
P is the applied force.
The Displacement of Applied force(P)=Circumference of the axle $= d = 2 \times π \times 12 c m = 24 π \times 10^{- 2} m$ $=d=2xxpixx12cm=24pixx10^-2m$
The working principle of wheel -axle system may be compared with the working principle of First Kind of lever

So
$P \times R = W \times r \Rightarrow P = W \times \frac{r}{R} = 5 \times 9.8 \times \frac{12}{38} N$ $PxxR=Wxxr=>P=Wxxr/R=5xx9.8xx12/38N$

Hence the Work done $= P \times d = 5 \times 9.8 \times \frac{12}{38} \times 24 π \times 10^{- 2} J = 11.7 J$ $=Pxxd=5xx9.8xx12/38xx24pixx10^-2J=11.7J$

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An object with a mass of $5 k g$ $5 kg$ is hanging from an axle with a radius of $12 c m$ $12 cm$ . If the wheel attached to the axle has a radius of $38 c m$ $38 cm$ , how much work would it take to turn the wheel a length equal to the circumference of the axle?

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An object with a mass of 5kg5 kg is hanging from an axle with a radius of 12cm12 cm. If the wheel attached to the axle has a radius of 38cm38 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

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An object with a mass of $5 k g$ $5 kg$ is hanging from an axle with a radius of $12 c m$ $12 cm$ . If the wheel attached to the axle has a radius of $38 c m$ $38 cm$ , how much work would it take to turn the wheel a length equal to the circumference of the axle?